DlocalizeAll -- localization of a D-module (extended version)

Synopsis

Usage:
DlocalizeAll(M,f), DlocalizeAll(I,f)
Inputs:
- M, a module, over the Weyl algebra D
- I, an ideal, which represents the module M = D/I
- f, a ring element, a polynomial
Optional inputs:
- Strategy => ..., -- strategy for computing a localization of a D-module
Outputs:
- a hash table, which contains the localized moduleM_f = M[f^-1] and some additional information

Description

An extension of Dlocalize that in addition computes the localization map, the b-function, and the power s of the generator f^s.

i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]

o1 = W

o1 : PolynomialRing

i2 : M = W^1/(ideal(x*Dx+1, Dy))

o2 = cokernel | xDx+1 Dy |

                            1
o2 : W-module, quotient of W

i3 : f = x^2-y^3

        3    2
o3 = - y  + x

o3 : W

i4 : DlocalizeAll(M, f)

o4 = HashTable{GeneratorPower => -2                                        }
                                                    4      5      5      7
               IntegrateBfunction => (s)(s + 1)(s + -)(s + -)(s + -)(s + -)
                                                    3      3      6      6
               LocMap => | y6-2x2y3+x4 |
               LocModule => cokernel | 3xDx+2yDy+15 y3Dy-x2Dy+6y2 |

o4 : HashTable

Ways to use `DlocalizeAll` :

DlocalizeAll(Ideal,RingElement)
DlocalizeAll(Module,RingElement)

DlocalizeAll -- localization of a D-module (extended version)

Synopsis

Description

See also

Ways to use DlocalizeAll :

Ways to use `DlocalizeAll` :